As is known, when two windings or, generally, any two conductors, are placed side-by-side in close proximity and the first is powered with an AC current, the second will develop an EMF according to Faraday's law. This EMF is developed via the magnetic field created from the current travelling in the first conductor. The EMF will accordingly cause current to flow in the second winding via the relation I1N1=I2N2, where I represents the current in each respective winding and N represents the number of turns in each winding.
In the case of a transformer, the ends of the second (or “secondary”) winding are closed to form a complete circuit. Moreover, the current induced in the second winding also produces a magnetic field, but this field will oppose the field produced by the first winding in accordance with Lenz' law.
In many transformers, the common centre is occupied by iron in a closed loop. This is done to present a path of least reluctance for the closed lines of magnetic field to flow. This path is commonly referred to as a low reactance path.
The component of the net magnetic field which does not follow the path of least reluctance is denoted the “magnetic field”. However, as will be appreciated by the skilled addressee, this is also known as the “leakage field” or “transformer magnetic field”. The magnetic field is not strictly uniform; for the most part, it is concentrated between the windings and acts substantially in an axial direction relative to the windings.
Since both transformer windings generate opposing magnetic fields, a cancellation occurs—at least to some degree—that results in a net leakage flux. The net leakage flux may be reduced by minimising the distance between the primary and secondary windings or, if there are more than two windings, by minimising the maximum separation between any two of them, while allowing sufficient electrical insulation between them.
The net leakage flux results in AC losses when superconducting materials are employed due to the AC nature of the current and voltage. In essence, these losses result because superconductor material is inherently a “non-reversible” material, and possesses a hysteresis loop of finite area. AC losses fall into the following three categories: hysteresis losses; coupling currents; and eddy currents.
Hysteresis losses develop due to the non-reversible magnetisation of the superconductor in a time varying magnetic field. In the sinusoidal steady state (SSS) characterised by a certain frequency, hysteresis losses are substantially fixed with respect to that frequency. However, hysteresis losses depend, in a complex way, on the arrangement of the conductors and the magnitude and direction of the magnetic field.
In general, it has been found that hysteresis losses are often proportional to the first or second power of a magnetic field reduction.
Coupling currents result from time-varying electrical fields, and represent loops of current where part of the loop is through a superconducting medium and part through a normally conductive medium. For example, coupling currents arise in a multi-filament twisted superconducting tape in a metal, or metal alloy, matrix in a 20 mT to 80 mT magnetic field. As the loops of coupling current cross through this medium, a resistive power loss—that is, the coupling current loss—results.
In the SSS, and between 20 mT and 80 mT, the coupling current loss associated with a multi-filament twisted superconducting tape is proportional to the square of the magnetic field amplitude. Outside this range, twisted filaments do not decouple and, therefore, there are no coupling currents and no coupling current losses.
The final substantial source of losses result from eddy currents. Eddy currents result from loops of current that flow entirely in the conducting material and thereby exhibit conventional resistive losses.
Eddy current losses in the SSS, expressed injoules per cubic metre, are proportional to the square of the magnetic field (as well as to the second power of the frequency). Hence, halving the magnetic field will reduce the eddy current losses by a factor of four.
Design principles are generally employed to render eddy current losses very small compared to superconductor losses, which is particularly true in the design of conventional transformers. Since eddy current loss can generally be reduced to a small component of the total AC loss by using well-established techniques, this document largely focuses on hysteresis losses and coupling current losses—which are collectively referred to as “superconductor losses” (or “superconductor loss”).
Superconductor loss (that is, the sum of hysteresis loss and coupling current loss) obeys well understood laws when the superconductors are comprised of straight filament tapes and/or when the superconductor is exposed to a magnetic field amplitude less than about 20 mT or greater than about 80 mT. Straight filament tapes are those where the filaments are parallel to the axis of the conductor itself.
In these scenarios, superconductor loss merely demonstrates a linear relationship with magnetic field. For example, reducing the magnetic field by half merely results in a halving of superconductor loss.
The reason the effect is merely linear is because the superconductor loss reduction in these scenarios is composed almost entirely of hysteresis loss. Unfortunately, the coupling loss is only negligible.
It is possible to reduce superconducting losses significantly by employing certain techniques. Two techniques are: twisting, to reduce hysteresis losses; and the use of highly resistive matrix materials, to reduce coupling current losses.
Hysteresis losses are able to be reduced by a factor of 2 to 6 by imparting a twist into the filaments of a superconductor. In essence, when twisted, the individual filaments behave magnetically as distinct units rather than as a large “block” since each does not occupy any one place within the cross section of matrix. Importantly, such reductions are only achievable in a limited window between 20 mT and 80 mT. The actual loss being largely dependent on the twist pitch employed, and the number of layers of filaments within the superconductor.
On a related note, the twist pitch is ideally chosen to be as small as possible, but a twist pitch significantly smaller than the nominal dimension of the superconductor (for example, the diameter of a wire, or the width of a tape) will degrade its current carrying capacity. Experimentally and theoretically, the minimum of twist capable of reducing hysteresis losses has been found to be in the of 4 to 6 mm range.
The employment of highly resistive matrix materials has been shown to reduce coupling current losses. Although the scientific understanding of why some matrix materials are more effective than others is not fully understood, it is believed that it is best to increase the matrix resistivity as much as possible to block the lossy coupling currents from flowing.
There are certain limitations inherent in the above mentioned loss reduction techniques. For example, these methods only reduce superconducting losses within a limited magnetic field amplitude range of 20 mT to 80 mT; a window far too small to be effective in a large power transformers (which typically deliver more than 10 MVA and generate magnetic fields between 200 mT and 500 mT).
The above discussion of the prior art is intended to provide the addressee with some context and is not to be taken as an admission of the state of common general knowledge in the art.